Question

what is the smallest number by which the number 222264 is to be divided such that the quotient becomes a perfect cube?

Answer 1

222264=2*2*2*3*3*3*3*7*7*7

3 is the least number which such that quotient becomes a perfect cube.

Check:

222264/3 = 74088

cube root(74088) = 42

Answer is 4

Hope it helps

Answer 2

First we have to find the Prime factorization of 222264


222264 =( 2 × 2 × 2 )×(3× 3 ×3 )× 3 ×( 7×7×7)


222264 = 2³ ×3³ × 3¹ × 7³


2³ , 3³ & 7³ are perfect cubes, so their product is also a perfect cube. The non-cube factor is 3.

Hence , the smallest number that we should divide 222264 to get a perfect cube is 3.

Check: 222264/ 3 = 74088 which is (42)³ - a perfect cube.

==================================================================

Hope this will help you....